| |

| |

Algebra Review | |

| |

| |

Real Numbers | |

| |

| |

Exponents and Radicals | |

| |

| |

Multiplying and Factoring Algebraic Equations | |

| |

| |

Rational Expressions | |

| |

| |

Solving Polynomial Equations | |

| |

| |

Solving Miscellaneous Equations | |

| |

| |

| |

Functions and Linear Models | |

| |

| |

Functions from the Numerical and Algebraic Viewpoints | |

| |

| |

Functions from the Graphical Viewpoint | |

| |

| |

Linear Functions | |

| |

| |

Linear Models | |

| |

| |

Linear Regression | |

| |

| |

Key Concepts | |

| |

| |

Review Exercises | |

| |

| |

Case Study: Modeling Spending on Internet Advertising | |

| |

| |

Technology Guides | |

| |

| |

Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions | |

| |

| |

| |

Systems of Linear Equations and Matrices | |

| |

| |

Systems of Two Equations in Two Unknowns | |

| |

| |

Using Matrices to Solve Systems of Equations | |

| |

| |

Applications of Systems of Linear Equations | |

| |

| |

Key Concepts | |

| |

| |

Review Exercises | |

| |

| |

Case Study: The Impact of Regulating Sulfur Emissions | |

| |

| |

Technology Guides | |

| |

| |

| |

Matrix Algebra and Applications | |

| |

| |

Matrix Addition and Scalar Multiplication | |

| |

| |

Matrix Multiplication | |

| |

| |

Matrix Inversion | |

| |

| |

Matrices in Practice: Game Theory | |

| |

| |

Matrices in Practice: Input-Output Models | |

| |

| |

Key Concepts | |

| |

| |

Review Exercises | |

| |

| |

Case Study: The Japanese Economy | |

| |

| |

Technology Guides | |

| |

| |

| |

Linear Programming | |

| |

| |

Graphing Linear Inequalities | |

| |

| |

Solving Linear Programming Problems Graphically | |

| |

| |

The Simplex Method: Solving Standard Maximization Problems | |

| |

| |

The Simplex Method: Solving General Linear Programming Problems | |

| |

| |

The Simplex Method and Duality (Optional) | |

| |

| |

Key Concepts | |

| |

| |

Review Exercises | |

| |

| |

Case Study: Airline Scheduling | |

| |

| |

Technology Guides | |

| |

| |

| |

The Mathematics of Finance | |

| |

| |

Simple Interest | |

| |

| |

Compound Interest | |

| |

| |

Annuities, Loans, and Bonds | |

| |

| |

Key Concepts | |

| |

| |

Review Exercises | |

| |

| |

Case Study: Saving for College | |

| |

| |

Technology Guides | |

| |

| |

| |

Sets and Counting | |

| |

| |

Sets and Set Operations | |

| |

| |

Cardinality | |

| |

| |

The Addition and Multiplication Principles | |

| |

| |

Permutations and Combinations | |

| |

| |

Key Concepts | |

| |

| |

Review Exercises | |

| |

| |

Case Study: Designing a Puzzle | |

| |

| |

Technology Guides | |

| |

| |

| |

Probability | |

| |

| |

Sample Spaces and Events | |

| |

| |

Estimated Probability | |

| |

| |

Theoretical Probability and Probability Distributions | |

| |

| |

Probability and Counting Techniques (optional) | |

| |

| |

Conditional Probability and Independence | |

| |

| |

Bayes' Theorem and Applications | |

| |

| |

Probability in Practice: Markov Systems | |

| |

| |

Key Concepts | |

| |

| |

Review Exercises | |

| |

| |

Case Study: The Monty Hall Problem | |

| |

| |

Technology Guides | |

| |

| |

| |

Random Variables and Statistics | |

| |

| |

Random Variables and Distributions | |

| |

| |

Bernoulli Trials and Binomial Random Variables | |

| |

| |

Measures of Central Tendency | |

| |

| |

Measures of Dispersion | |

| |

| |

Normal Distributions | |

| |

| |

Key Concepts | |

| |

| |

Review Exercises | |

| |

| |

Case Study: Spotting Tax Fraud with Benford's Law | |

| |

| |

Technology Guides | |

| |

| |

Optional Internet Topics: Sampling Distributions and the Central Limit Theorem | |

| |

| |

Confidence Intervals | |

| |

| |

Hypothesis Testing | |

| |

| |

| |

Nonlinear Models | |

| |

| |

Quadratic Functions and Models | |

| |

| |

Exponential Functions and Models | |

| |

| |

Logarithmic Functions and Models | |

| |

| |

Logistic Functions and Models | |

| |

| |

Key Concepts | |

| |

| |

Review Exercises | |

| |

| |

Case Study: Checking up on Malthus | |

| |

| |

Technology Guides | |

| |

| |

Optional Internet Topics: Inverse Functions | |

| |

| |

Using and Deriving Algebraic Properties of Logarithms | |

| |

| |

| |

Introduction to the Derivative | |

| |

| |

Limits: Numerical and Graphical Approaches | |

| |

| |

Limits and Continuity | |

| |

| |

Limits: Algebraic Approach | |

| |

| |

Average Rate of Change | |

| |

| |

Derivatives: Numerical and Graphical Viewpoints | |

| |

| |

Derivatives: Algebraic Viewpoint | |

| |

| |

Derivatives of Powers, Sums, and Constant Multiples | |

| |

| |

A First Application: Marginal Analysis | |

| |

| |

Key Concepts | |

| |

| |

Review Exercises | |

| |

| |

Case Study: Reducing Sulfur Emissions | |

| |

| |

Technology Guides | |

| |

| |

Optional Internet Topics: Sketching the Graph of the Derivative | |

| |

| |

Proof of the Power Rule | |

| |

| |

Continuity and Differentiability | |

| |

| |

| |

Techniques of Differentiation | |

| |

| |

The Product and Quotient Rules | |

| |

| |

The Chain Rule | |

| |

| |

Derivatives of Logarithmic and Exponential Functions | |

| |

| |

Implicit Differentiation | |

| |

| |

Key Concepts | |

| |

| |

Review Exercises | |

| |

| |

Case Study: Projecting Market Growth | |

| |

| |

Technology Guides | |

| |

| |

Optional Internet Topic: Linear Approximation and Error Estimation | |

| |

| |

| |

Applications of the Derivative | |

| |

| |

Maxima and Minima | |

| |

| |

Applications of Maxima and Minima | |

| |

| |

The Second Derivative and Analyzing Graphs | |

| |

| |

R | |